1. Field of the Invention
The present invention relates to quartz resonators and more particularly to resonators having good thermal properties, having a relatively low resonance frequency, vibrating in a fundamental torsion mode and being adapted to be mass-produced by chemical etching techniques.
2. Description of the Related Art
Resonators are known which meet the conditions of having small variation in frequency as a function of temperature, having a low resonance frequency and being chemically machined. Examples can be found in the following references:
(1) "New quartz tuning fork with very low temperature coefficient" B. Momosaki et al., appearing in the 33rd Annual Symposium on Frequency Control (A.S.F.C.), 1979, pp. 247-254. PA1 (2) "Vibration analysis of coupled flexural mode tuning fork type quartz crystal resonator" by H. Kawashimi, appearing in the 42nd A.S.F.C. 1988, pp. 45-52. PA1 (3) "A new low frequency thermally compensated contour mode resonator" by C. Bourgeois, appearing in the 44th A.S.F.C., 1990, pp. 367-371.
The three references above relate to resonators using coupling between two modes of vibration in order to improve the thermal properties. The first two references concern a tuning fork resonator vibrating in a flexural mode coupled to a torsion mode, while the third reference concerns a resonator vibrating in an elongation mode coupled to a flexural mode. The device of the three references described above are characterized by the use of relatively close coupling between the modes of vibration. By close coupling there is understood a relatively small frequency difference (&lt;2%) between the non-coupled modes. A result of this close coupling is that the resulting thermal properties depend critically on certain geometrical dimensions; this considerably reduces the yield in the manufacture of such resonators and restricts practical interest.